Mittag-Leffler and Padé approximations to stiff fractional two point kinetics equations

The mathematical model of stiff two-point kinetics equations for a compact core with bulky reflector plays a basic role in kinetics schemes of reflector reactor in the nuclear reactor dynamic systems. This model is a non-conventional models describe the number of neutrons per volume and delayed precursor into reactors. To analyze reactor response, a novel mathematical treatment should be introduced to solve the stiff fractional differential equations in the matrix form. Mittag-Leffler functions have recently caught the interest, particularly with the models which using fractional calculus. In this work, a fractional formula of the coupled stiff two-point reactor kinetics model with I-groups of delayed neutrons are considered by merging Mittag-Leffler function with the developed Padé approximations. The validity of the proposed fractional formula is confirmed for various reactivity such as step and ramp reactivity in various fractional order. The estimated values confirm that the treatment for the problem under consideration using Mittag-Leffler function and the developed Padé approximations agree with Picard iteration method and the conformist techniques.